{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:77G3QJJ52EXKPRARS6RRT24N7O","short_pith_number":"pith:77G3QJJ5","canonical_record":{"source":{"id":"1705.00685","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-05-01T19:51:57Z","cross_cats_sorted":[],"title_canon_sha256":"3844397ebae5142d5e0bc79077e30b801f4c254fb9504f40c62180635f225c07","abstract_canon_sha256":"9aed728635f2769aa3d79e7b71f118b2d43578bc3e66f86d83869f7b5024a0b0"},"schema_version":"1.0"},"canonical_sha256":"ffcdb8253dd12ea7c41197a319eb8dfb8727c3b6ef290199cf06c05416686303","source":{"kind":"arxiv","id":"1705.00685","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.00685","created_at":"2026-05-18T00:45:10Z"},{"alias_kind":"arxiv_version","alias_value":"1705.00685v1","created_at":"2026-05-18T00:45:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.00685","created_at":"2026-05-18T00:45:10Z"},{"alias_kind":"pith_short_12","alias_value":"77G3QJJ52EXK","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_16","alias_value":"77G3QJJ52EXKPRAR","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_8","alias_value":"77G3QJJ5","created_at":"2026-05-18T12:31:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:77G3QJJ52EXKPRARS6RRT24N7O","target":"record","payload":{"canonical_record":{"source":{"id":"1705.00685","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-05-01T19:51:57Z","cross_cats_sorted":[],"title_canon_sha256":"3844397ebae5142d5e0bc79077e30b801f4c254fb9504f40c62180635f225c07","abstract_canon_sha256":"9aed728635f2769aa3d79e7b71f118b2d43578bc3e66f86d83869f7b5024a0b0"},"schema_version":"1.0"},"canonical_sha256":"ffcdb8253dd12ea7c41197a319eb8dfb8727c3b6ef290199cf06c05416686303","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:45:10.153565Z","signature_b64":"SKbbapgPqo5BKfWTsyVpuunI85W7YDINRxzcdDFAWKy3Lpy6b9+Rfbti78AjEOLgocpi6l6I+6ZOVf4Uy0+rDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ffcdb8253dd12ea7c41197a319eb8dfb8727c3b6ef290199cf06c05416686303","last_reissued_at":"2026-05-18T00:45:10.152680Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:45:10.152680Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1705.00685","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:45:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qpuvaHB+j5UUsQaI8VDV/0M/2bwpogluLF7ik8CpfrYyvaYHgy4i7M8Q2qyG/E7GyZjKT4xMXtmZgJA5F7D/Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T10:31:09.246694Z"},"content_sha256":"5a8c2438c5765801e72d1209a24a7860c0fd1d53aa3c17534f3f792fe81f2462","schema_version":"1.0","event_id":"sha256:5a8c2438c5765801e72d1209a24a7860c0fd1d53aa3c17534f3f792fe81f2462"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:77G3QJJ52EXKPRARS6RRT24N7O","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Classification of $\\delta(2,n-2)$-ideal Lagrangian submanifolds in $n$-dimensional complex space forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Bang-Yen Chen, Franki Dillen, Joeri Van der Veken, Luc Vrancken","submitted_at":"2017-05-01T19:51:57Z","abstract_excerpt":"It was proven in [B.-Y. Chen, F. Dillen, J. Van der Veken and L. Vrancken, Curvature inequalities for Lagrangian submanifolds: the final solution, Differ. Geom. Appl. 31 (2013), 808-819] that every Lagrangian submanifold $M$ of a complex space form $\\tilde M^{n}(4c)$ of constant holomorphic sectional curvature $4c$ satisfies the following optimal inequality: \\begin{align*} \\delta(2,n-2) \\leq \\frac{n^2(n-2)}{4(n-1)} H^2 + 2(n-2) c, \\end{align*} where $H^2$ is the squared mean curvature and $\\delta(2,n-2)$ is a $\\delta$-invariant on $M$. In this paper we classify Lagrangian submanifolds of compl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.00685","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:45:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rlGdjOFDEMDRF9UOu7fMG3N81cbMDlKvzakSmt7CN3ELZPWrZg1f7oeNcwpyVCBL6qyoDHkbU/rwKE8ew179Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T10:31:09.247048Z"},"content_sha256":"ffb815d805e11c74bda2582d6d50203c1bb91fd82ea072dd976f8e5c1771e999","schema_version":"1.0","event_id":"sha256:ffb815d805e11c74bda2582d6d50203c1bb91fd82ea072dd976f8e5c1771e999"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/77G3QJJ52EXKPRARS6RRT24N7O/bundle.json","state_url":"https://pith.science/pith/77G3QJJ52EXKPRARS6RRT24N7O/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/77G3QJJ52EXKPRARS6RRT24N7O/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-01T10:31:09Z","links":{"resolver":"https://pith.science/pith/77G3QJJ52EXKPRARS6RRT24N7O","bundle":"https://pith.science/pith/77G3QJJ52EXKPRARS6RRT24N7O/bundle.json","state":"https://pith.science/pith/77G3QJJ52EXKPRARS6RRT24N7O/state.json","well_known_bundle":"https://pith.science/.well-known/pith/77G3QJJ52EXKPRARS6RRT24N7O/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:77G3QJJ52EXKPRARS6RRT24N7O","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"9aed728635f2769aa3d79e7b71f118b2d43578bc3e66f86d83869f7b5024a0b0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-05-01T19:51:57Z","title_canon_sha256":"3844397ebae5142d5e0bc79077e30b801f4c254fb9504f40c62180635f225c07"},"schema_version":"1.0","source":{"id":"1705.00685","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.00685","created_at":"2026-05-18T00:45:10Z"},{"alias_kind":"arxiv_version","alias_value":"1705.00685v1","created_at":"2026-05-18T00:45:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.00685","created_at":"2026-05-18T00:45:10Z"},{"alias_kind":"pith_short_12","alias_value":"77G3QJJ52EXK","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_16","alias_value":"77G3QJJ52EXKPRAR","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_8","alias_value":"77G3QJJ5","created_at":"2026-05-18T12:31:03Z"}],"graph_snapshots":[{"event_id":"sha256:ffb815d805e11c74bda2582d6d50203c1bb91fd82ea072dd976f8e5c1771e999","target":"graph","created_at":"2026-05-18T00:45:10Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"It was proven in [B.-Y. Chen, F. Dillen, J. Van der Veken and L. Vrancken, Curvature inequalities for Lagrangian submanifolds: the final solution, Differ. Geom. Appl. 31 (2013), 808-819] that every Lagrangian submanifold $M$ of a complex space form $\\tilde M^{n}(4c)$ of constant holomorphic sectional curvature $4c$ satisfies the following optimal inequality: \\begin{align*} \\delta(2,n-2) \\leq \\frac{n^2(n-2)}{4(n-1)} H^2 + 2(n-2) c, \\end{align*} where $H^2$ is the squared mean curvature and $\\delta(2,n-2)$ is a $\\delta$-invariant on $M$. In this paper we classify Lagrangian submanifolds of compl","authors_text":"Bang-Yen Chen, Franki Dillen, Joeri Van der Veken, Luc Vrancken","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-05-01T19:51:57Z","title":"Classification of $\\delta(2,n-2)$-ideal Lagrangian submanifolds in $n$-dimensional complex space forms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.00685","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:5a8c2438c5765801e72d1209a24a7860c0fd1d53aa3c17534f3f792fe81f2462","target":"record","created_at":"2026-05-18T00:45:10Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"9aed728635f2769aa3d79e7b71f118b2d43578bc3e66f86d83869f7b5024a0b0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-05-01T19:51:57Z","title_canon_sha256":"3844397ebae5142d5e0bc79077e30b801f4c254fb9504f40c62180635f225c07"},"schema_version":"1.0","source":{"id":"1705.00685","kind":"arxiv","version":1}},"canonical_sha256":"ffcdb8253dd12ea7c41197a319eb8dfb8727c3b6ef290199cf06c05416686303","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ffcdb8253dd12ea7c41197a319eb8dfb8727c3b6ef290199cf06c05416686303","first_computed_at":"2026-05-18T00:45:10.152680Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:45:10.152680Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SKbbapgPqo5BKfWTsyVpuunI85W7YDINRxzcdDFAWKy3Lpy6b9+Rfbti78AjEOLgocpi6l6I+6ZOVf4Uy0+rDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:45:10.153565Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.00685","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5a8c2438c5765801e72d1209a24a7860c0fd1d53aa3c17534f3f792fe81f2462","sha256:ffb815d805e11c74bda2582d6d50203c1bb91fd82ea072dd976f8e5c1771e999"],"state_sha256":"0610479585b451443bedad690d78600fbba1ec9057e06ce2775195726c218d81"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2Mm6g6peIYSWnGJUmjR23MrTJmadN35X2os9Du6nQAy/vNmLb+xTHa9UXoaAL2LdHyBUpZ+ESYoI3TBD7MScDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T10:31:09.249017Z","bundle_sha256":"164264475eca69a2c460fa370a672b0732ea253c3808514e4a676afcdc664499"}}